Wave-vortex mode coupling in neutrally stable baroclinic flows

Abdelaziz Salhi and Alexandre B. Pieri
Phys. Rev. E 90, 043003 – Published 7 October 2014

Abstract

Rotating stratified flows in thermal wind balance are at the center of geophysical fluid dynamics. Recently, endeavors were put on studying the linear response of such flows to potential vorticity perturbations. It has been shown that the initial potential vorticity (PV) distribution is fundamental and is responsible for important transient growth of the perturbation and gravity-wave generation. Using Pfeiffer's theorem [J. Differ. Equat. 11, 145 (1972)], we give the mathematical demonstration of the stability of asymmetric perturbations k10 of a uniform, unbounded flow in thermal wind balance. Incidentally, we prove that both the wave mode (that corresponds to a vanishing PV) and the vortex mode (corresponding to a nonzero PV) are stable. The emphasis is put on the nontrivial behavior of inertia-gravity waves (IGWs) when deformed by a background shear. In particular, we show that in the linear limit, sheared inertia-gravity waves asymptotically oscillate at the inertial waves frequency, but their amplitude is sensitive to shear, stratification, and rotation. Last, we study the development of the IGWs dynamics considering isotropic initial conditions. Computations indicate that both the vortex mode and the wave mode generate IGWs, but the energy of the IGWs generated by the vortex mode is more important than the energy of the IGWs generated by the wave mode. It is also found that, at large times, the energy of the IGWs generated by the vortex mode increases as the ratio kv/kh (initial vertical wavenumber over horizontal wavenumber) increases (like kv2/kh2), while the energy of the IGWs generated by the wave mode oscillates in function of kv/kh.

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  • Received 20 January 2014
  • Revised 30 May 2014

DOI:https://doi.org/10.1103/PhysRevE.90.043003

©2014 American Physical Society

Authors & Affiliations

Abdelaziz Salhi1,2 and Alexandre B. Pieri3,*

  • 1Département de Physique, Faculté des sciences de Tunis, 1060 Tunis, Tunisia
  • 2Institute for Advanced Study (IMéRA fellow), Université Aix-Marseille, 2 Place Le Verrier 13004 Marseille, France
  • 3Institute of the Atmospheric Sciences and Climate, Corso Fiume 4, 10133 Turin, Italy

  • *a.pieri@isac.cnr.it

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Vol. 90, Iss. 4 — October 2014

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